Figure gives the x-t plot of a particle executing one-dimensional . . .

Question :  Figure gives the x-t plot of a particle executing one-dimensional simple  harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.

Doubt by Shruti

Solution : 

In chapter 14, we will discuss Simple Harmonic Motion in detail. 
Here we need to know that the acceleration of SHM is given by 
a=-ω²x

So, acceleration (a) is opposite to position (x)

i) At t=0.3 sec

From the graph it is clear that at t=0.3 sec
✅Position (x) : The curve is below the time axis → x<0 [Negative]

✅Velcoity (v) : Slope is going downward → v<0 [Negative]

✅Acceleration: Opposite to position → a>0 [Positive]

ii) At t=1.2 s

✅Position (x) : The curve is above the time axis → x>0 [Positive]

✅Velcoity (v) : Slope is going upward → v>0 [Positive]

✅Acceleration: Opposite to position → a<0 [Negative]

(iii) At t=-1.2 s

✅Position (x) : The curve is below the time axis → x<0 [Negative]

✅Velcoity (v) : Slope is going downward so position is negative but in this case time is also negative so velocity will be positive.
→ v>0 [Positive]

✅Acceleration: Opposite to position → a>0  [Positive]

Final Answers

At t=0.3 s

x=Negative, v=Negative, a=Positive 
At t=1.2 s

x=Positive, v=Positive, a=Negative
At t=-1.2s
x=Negative, v=Positive, a=Positive